Which one would be the preposition of choice when discussing the number of times something happened? Examples:
I saw her for the third time. She is visiting me for the first time.
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Anytime you refer to time at all, you will use
If you were to say
Escribí una caricatura para tres minutos
It would suggest that you drew a cartoon FOR 3 minutes, not as in time, but rather, for, as in a gift. In other words you would be drawing a cartoon as a favor to 3 Minutes, as if it were a person/business/entity/etcetera... named "3 Minutes"